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Table 6: Index Permutation (5, 4, 7, 9, 3, 8, 1, 0, 2, 6) [1]

If we assume that the control rotors generate random permutations, the expected number of 

steps for a given cipher rotor i depends only on the number control rotor output letters that 

feed into cipher rotor C

i

. The list of all 45 input pairs and their corresponding number of 

letters is show in Table 7. If a sufficient amount of plaintext is known, we can obtain 

information related to the Count column of Table 7 for each cipher rotor based on a count 

of the number of times that cipher rotor i has stepped. From this count, we can make 

restrictions on the index permutation using the Pairs column.

We can estimate the amount of plaintext that is needed in the following manner. Each 

cipher rotor is connected to k control rotor outputs, where 1 

≤

 k 

≤

 11. We can determine the 

expected stepping ratios for a rotor connected to exactly k control rotor outputs. These will 

sum up to a value greater than one since more than one rotor generally steps. To compute 

the ratios, we assume all control rotor outputs to be equally likely and generate all 

















26

4

= 

25

---

14,950 outputs, counting the number of times that at least one element of each pair in Table 

7 occurs. Table 8 shows the results, where Step Ratio is obtained by dividing the Step 

Count column by 14,950. Note that these results are independent of the actual index rotor 

permutation.

Letters Count Pairs

1

3

(0,1) (0,2) (0,9)

2

4

(0,3) (1,2) (1,9) (2,9)

3

5

(0,4) (0,5) (1,3) (2,3) (3,9)

4

7

(0,6) (1,5) (2,5) (5,9) (1,4) (2,4) (4,9)

5

6

(0,7) (1,6) (2,6) (6,9) (3,4) (3,5)

6

6

(0,8) (1,7) (2,7) (7,9) (3,6) (4,5)

7

6

(1,8) (2,8) (8,9) (3,7) (4,6) (5,6)

8

3

(3,8) (4,7) (5,7)

9

3

(4,8) (5,8) (6,7)

10

1

(6,8)

11

1

(7,8)

Table 7: Index Permutation Input Pairs [1]

Letters Example Pairs Step Count Step Ratio

1

(0,1)

2,300

0.1538462

2

(0,3)

4,324

0.2892308

3

(0,4)

6,095

0.4076923

4

(0,6)

7,635

0.5107023

5

(0,7)

8,965

0.5996656

6

(0,8)

10,105

0.6759197

7

(1,8)

11,074

0.7407358

8

(3,8)

11,890

0.7953177

9

(4,8)

12,570

0.8408027

10

(6,8)

13,130

0.8782609

11

(7,8)

13,585

0.9086957